Some asymptotic formulas for the Bogoliubov Gaussian measure

We consider problems of integrating over the Bogoliubov measure in the space of continuous functions and obtain asymptotic formulas for one class of Laplace-type functional integrals with respect to the Bogoliubov measure. We also prove related asymptotic results concerning large deviations for the Bogoliubov measure. For the basic functional, we take the $L^p$ norm and establish that the Bogoliubov trajectories are Hölder-continuous of order $\gamma<1/2$.